The electric potential as a function of $x,y$ is given by $V = 5\left( x^{2} - y^{2} \right)V$. The

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The electric potential as a function of $x,y$ is given by $V = 5\left( x^{2} - y^{2} \right)V$. The electric field at a point $(2,3)m$ is $\_\_\_\_$ V/m.

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Sol. [Key Concept: $E = - 
abla\ V$ with $V = 5(x^{2} - y^{2})$ gives $E_{x} = - 10x,\ E_{y} = 10y$; at $(2,3)$ this is $( - 20,30)$ V/m.]$$V = 5\left( x^{2} - y^{2} ight)V$$$$\begin{matrix} & \varepsilon_{x} = \frac{- dv}{dx} = - 10x\widehat{i} \ & \varepsilon_{y} = \frac{- dv}{dx} = + 10y\widehat{i} \Rightarrow \varepsilon(2,3) = - 20\widehat{i} + 30\widehat{j} \end{matrix}$$

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